> Of course, there are subtle implications of how it will be implemented

Indeed.  Ideally, as you mention, the implementation would only use __lt__ (as with sort and bisect).  I think that constraint only leaves one reasonable choice: namely, max and min for multiple args would be functionally equivalent to max_list and min_list below:

def min2(x, y):
    return y if y < x else x

def max2(x, y):
    return x if y < x else y

def min_list(xs):
    return reduce(min2, xs)

def max_list(xs):
    return reduce(max2, xs)